Understanding the effects of Doppler phenomena in white light Fabry–Perot interferometers for simultaneous position and velocity measurement

Abstract

In static tests, low-power (<5 mW) white light extrinsic Fabry-Perot interferometric position sensors offer high-accuracy (μm) absolute measurements of a target's position over large (cm) axial-position ranges, and since position is demodulated directly from phase in the interferogram, these sensors are robust to fluctuations in measured power levels. However, target surface dynamics distort the interferogram via Doppler shifting, introducing a bias in the demodulation process. With typical commercial off-the-shelf hardware, a broadband source centered near 1550 nm, and an otherwise typical setup, the bias may be as large as 50-100 μm for target surface velocities as low as 0.1 mm/s. In this paper, the authors derive a model for this Doppler-induced position bias, relating its magnitude to three swept-filter tuning parameters. Target velocity (magnitude and direction) is calculated using this relationship in conjunction with a phase-diversity approach, and knowledge of the target's velocity is then used to compensate exactly for the position bias. The phase-diversity approach exploits side-by-side measurement signals, transmitted through separate swept filters with distinct tuning parameters, and permits simultaneous measurement of target velocity and target position, thereby mitigating the most fundamental performance limitation that exists on dynamic white light interferometric position sensors.

A Demodulation Model of Dynamic Low-Finesse Fabry-Perot Cavity Based on the Instantaneous Frequency

“…When the OPL changes during the spectrum acquisition process, it will cause the famous Doppler phenomenon, resulting in a Doppler-induced demodulation error. From the view of the frequency domain, the Doppler-induced error has been discussed in reference [19]. Based on our model, we are going to discuss it from the perspective of the wavenumberfrequency domain.…”

“…where f start and f stop are respectively the light frequencies of the interference spectrum's first and last data points. The reference [19] also gave a Doppler-induced demodulation error formula as follows…”

“…In other words, the OPL of the FP cavity should be kept constant during the spectrum acquisition process. Otherwise, the famous Doppler phenomena [19] will distort the interference spectrum, leading to a big demodulation error, even demodulation failure. For this reason, these algorithms are only suitable for the measurement of the relative static measurand.…”

Measurement of dynamic interferometer baseline perturbations by means of wavelength-scanning interferometry

“…7 The rapid slope of the baseline during the spectrum measurement time results in an abrupt approximation error. An approach overcoming this issue was proposed and implemented in 18 .…”

Fast interrogation of dynamic low‐finesse Fabry‐Perot interferometers: A review

“…Laser‐based absolute measurement method is a better choice for industrial applications. It should be noted that when the F‐P cavity changes during the laser wavelength scanning process, the acquired spectrum will be distorted, and the Doppler‐induced error will be hundreds of times the actual cavity length change 70,71 . Therefore, for the spectra collected by wavelength scanning, the conventional WLI algorithm is not applicable.…”